×

On the number of periodic reflecting rays in generic domains. (English) Zbl 0668.58005

Authors’ abstract: We prove that for generic domains \(\Omega \subset {\mathbb{R}}^ n\) with smooth boundary X for every integer \(s\geq 2\) there is at most a finite number of periodic reflecting rays with just s reflections on X.
Reviewer: J.Mihut

MSC:

58A99 General theory of differentiable manifolds
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Katok, Lecture Notes in Mathematics 1222 (1986)
[2] Katok, Ergod. Th. & Dynam. Sys. 2 pp 339– (1982)
[3] Golubitsky, Stable Mappings and their Singularities (1973)
[4] Stojanov, C.R. Acad. Bulgare Sci. 39 pp 13– (1986)
[5] Stojanov, Ergod. Th. Dynam. Sys. 7 pp none– (1987)
[6] DOI: 10.1007/BF01076325 · Zbl 0207.20305
[7] DOI: 10.2307/2374608 · Zbl 0652.35027
[8] DOI: 10.1080/03605308008820141 · Zbl 0435.35065
[9] DOI: 10.1007/BF01161919 · Zbl 0673.58035
[10] DOI: 10.1002/cpa.3160310504 · Zbl 0368.35020
[11] DOI: 10.1090/S0273-0979-1986-15445-5 · Zbl 0602.58050
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.